E E 2415
24
E E 2415 Lecture 15 Introduction to Frequency Response, Poles & Zeroes, Resonant Circuit
description
E E 2415. Lecture 15 Introduction to Frequency Response, Poles & Zeroes, Resonant Circuit. Low-Pass Filter Example: (1/2). Low-pass Filter:. Low-Pass Filter Example: (2/2). Gain in Decibels. Using the Low-pass filter example:. Drops at 20 db per decade. Bode Plot of Low-Pass Filter. - PowerPoint PPT Presentation
Transcript of E E 2415
E E 2415
Lecture 15Introduction to Frequency Response, Poles & Zeroes, Resonant Circuit
Low-Pass Filter Example: (1/2)
Low-pass Filter:
fo
inf
f
jCV
HjV RC
Low-Pass Filter Example: (2/2)
2
2
1tan
1o
o
H
Gain in Decibels
Using the Low-pass filter example:
Drops at 20 dbper decade
Bode Plot of Low-Pass Filter
Phase Plot of Low-Pass Filter
High-Pass Filter Example: (1/2)
fo
inf
f
RVH
jV RC
1
11
o o
o
o o
j j
Hj jj
High-Pass Filter Example: (2/2)
1
2
2
tan
1
o o
o
H
2
21
gaino
o
G H
1tan Phase ShiftoP
High-Pass Gain in Decibels
2
2
20
1
odb
o
G Log
0db oG
@20 /20 Rises db decadedb o
o
G Log
Bode Plot of High-Pass Filter
Phase Plot of High-Pass Filter
Definition: Poles & Zeroes
A zero at the origin
A pole at jw1
A zero at jw1
A pole at jw2
A pole at the origin
Effect of a Pole on the Bode Plot• A pole causes the
asymptotic slope to decrease by 20 db/decade.
• A pole at the origin causes the slope to start at –20 db/decade.
• A pole not at the origin causes a corner to appear at the pole’s frequency; then the slope is 20 db/decade less for frequencies greater than the pole’s frequency.
Effect of a Zero on the Bode Plot• A zero causes the
asymptotic slope to increase by 20 db/decade.
• A zero at the origin causes the slope to start at +20 db/decade.
• A zero not at the origin causes a corner to appear at the pole’s frequency; then the slope is 20 db/decade more for frequencies greater than the zero’s frequency.
Examples: (1/3)
A zero at the origin
A pole at jw1
Examples: (2/3)
A zero at jw1
A pole at jw2
A pole at the origin
Examples: (3/3)
Resonant Bandpass Filter (1/2)
Resonant Bandpass Filter (2/2)
Resonant BandPass Poles & Zeroes
Zero at origin
Two poles
Bode Plot for Resonant Bandpass
Phase Plot for Resonant Bandpass
Bandwidth of Resonant Bandpass (1/2)
at half power
Take square and reciprocal of both sides
Need both solutions for positive values of w
Bandwidth of Resonant Bandpass (2/2)
Positive w for -1
Positive w for +1
Bandwidth for a seriesresonant bandpassfilter
